What made Tyner's video so popular is that you can hear pretty clearly what the people involved in the encounter were saying and the tone of their interactions. The microphone on Tyner's phone captured sufficiently good audio to get the point across. Not all cell phones have good microphones, so make sure you record some test video -- in advance, probably before you get involved in a security confrontation -- so you know what to do. (More tips for cell phone audio recording.)
So if you're shooting video of a security encounter, keep talking; keep asking questions -- especially clarifying ones like "What are you doing?" rather than rhetorical ones like "Ever hear of the U.S. Constitution?"; let people answer you -- don't interrupt them or shout over them; and generally collect as much audio information as possible.
Note that Tyner apparently did not inform the TSA officials that he was recording the encounter, which may also be why he didn't point the phone at them. Recording police or security officers can be a legal gray area.
As Glenn Harlan Reynolds explained in "Popular Mechanics" earlier this year, taking photos is public places is not a crime. However, as Wendy McElroy explained in the blog, "The Freeman," 12 states currently have laws requiring that "all parties must consent for a recording to be legal -- unless, as with TV news crews, it is obvious to all that recording is underway."
Three of these states have taken this recording restriction a step further. According to McElroy, Illinois, Maryland and Massachusetts have specifically made it "illegal to record an on-duty police officer even if the encounter involves you and may be necessary to your defense, and even if the recording is on a public street where no expectation of privacy exists."
It's unclear whether this law also applies to other security officers such as TSA, transit police, or campus security.
Recording security or police officers in action definitely is not risk-free. Knowing your rights, the law in that state, location-specific policies like airport rules, your equipment, and recording technique basics can help you make the best decisions in these situations.